Question

A hummingbird is flying toward a large tree that has a radius of 6 feet. When it is 31 feet from the center of the tree, its lines of sight form two tangents. What is the measure of the arc on the tree that the hummingbird can see?

Answer 1

from diagram you can say
\[\cos A = \frac{6}{31}\]
the Arc is 2A
\[Arc = 2\cos^{-1} (\frac{6}{31})\]